Yes rabbit food can go bad, it depends on the best before date but also if its stored correctly as leaving it just opened and in the air or in direct sunlight will loose some vitamins and it may go stale.
I would get two food storage containers, one of them I would fill up and put in the freezer and then the other I would fill up and leave it near the hutchs for easy access, anymore thats left in the bag I would roll it up tightly and secure it. As reopening and closing the bag wont make it last as long.